基于改进的脉冲耦合神经网络模型的实时机器人路径规划资源-CSDN文库

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本文介绍了基于改进型脉冲耦合神经网络（MPCNN）模型的实时机器人路径规划方法。该模型是为了在非静态环境中进行移动机器人的实时碰撞自由路径规划而提出的。在提出的研究中，所涉及的神经网络是由具有局部横向连接的神经元组成的拓扑结构。此模型无需事先知道目标或障碍物的运动信息，即能动态地工作。传统的脉冲耦合神经网络（PCNNs）被广泛应用于图像处理领域，它们的生物神经网络基础允许神经元仅通过局部连接进行通信，从而使得波形传播类似于神经元之间的连接强度。这些模型在静态环境中表现良好，可以生成全局最短路径，但对动态环境的适应性较差。为了改善这些传统PCNN模型的性能，并使其能够更好地应用于机器人路径规划，研究者们提出了MPCNN模型。MPCNN模型中，目标神经元首先被激活，然后激活事件通过神经元之间的局部横向连接传播，像波一样扩散出去。障碍物与它们的邻居没有连接。每一个神经元记录其父节点，也就是导致其激活的邻居。然后，可以依据机器人到目标的父节点序列确定实时的最优路径。在静态环境中，障碍物和目标是静止的，MPCNN模型证明了网络中生成的波以与神经元之间连接强度成正比的传播时间向外扩散。因此，所生成的路径始终是从机器人到目标的全局最短路径。此外，提出模型中的每一个神经元都可以在不进行任何比较计算的情况下向其相邻的神经元传播激活事件。通过模拟和比较研究，验证了该方法的有效性和效率。MPCNN模型被应用于为移动机器人生成避障路径，解决迷宫型问题，绕过凹形U型障碍物，以及在障碍物变化的环境中跟踪移动目标。最终，该方法成功地解决了上述问题。本文还涉及了实时碰撞自由路径规划的概念。在机器人技术中，路径规划是指机器人从初始位置移动到目标位置的过程，它需要避免碰撞并考虑到环境中的各种约束。在非静态环境中，环境是动态变化的，可能包括移动的障碍物或目标，这就对路径规划算法提出了更高的要求。此外，关键词“碰撞避让”、“移动机器人”、“神经动态”、“路径规划”、“脉冲耦合神经网络”和“波”也被提及，这些关键词体现了该研究的主要内容和研究领域。脉冲耦合神经网络作为一种特殊的神经网络，在机器人路径规划领域具有独特的优势，特别是在动态变化环境中的实时规划。文章最后指出了这项研究的现实意义，它表明了MPCNN模型在动态环境下的机器人路径规划中的应用潜力。通过将其应用于解决多种类型的路径问题，MPCNN模型展现出了处理复杂情况的能力，并且有望在更广泛的实际应用中发挥作用。

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1724 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 11, NOVEMBER 2009

Real-Time Robot Path Planning Based on a Modiﬁed

Pulse-Coupled Neural Network Model

Hong Qu, Simon X. Yang, Senior Member, IEEE, Allan R. Willms, and Zhang Yi

Abstract—This paper presents a modiﬁed pulse-coupled

neural network (MPCNN) model for real-time collision-free path

planning of mobile robots in nonstationary environments. The

proposed neural network for robots is topologically organized

with only local lateral connections among neurons. It works in

dynamic environments and requires no prior knowledge of target

or barrier movements. The target neuron ﬁres ﬁrst, and then the

ﬁring event spreads out, through the lateral connections among

the neurons, like the propagation of a wave. Obstacles have no

connections to their neighbors. Each neuron records its parent,

that is, the neighbor that caused it to ﬁre. The real-time optimal

path is then the sequence of parents from the robot to the target.

In a static case where the barriers and targets are stationary, this

paper proves that the generated wave in the network spreads out-

ward with travel times proportional to the linking strength among

neurons. Thus, the generated path is always the global shortest

path from the robot to the target. In addition, each neuron in the

proposed model can propagate a ﬁring event to its neighboring

neuron without any comparing computations. The proposed

model is applied to generate collision-free paths for a mobile robot

to solve a maze-type problem, to circumvent concave U-shaped

obstacles, and to track a moving target in an environment with

varying obstacles. The effectiveness and efﬁciency of the proposed

approach is demonstrated through simulation and comparison

studies.

Index Terms—Collision avoidance, mobile robot, neural dy-

namics, path planning, pulse-coupled neural networks (PCNNs),

spiking, wave.

I. INTRODUCTION

EAL-TIME planning of a collision-free path for a mobile

robot to move from an initial position to a target position

in a nonstationary environment is a well-known problem in

robotics. Since the earliest work by Lozano-Perez and Wesley

Manuscript received December 01, 2007; revised April 23, 2009 and July

27, 2009; accepted July 30, 2009. First published September 22, 2009; current

version published November 04, 2009. This work was supported by the National

Science and Engineering Research Council (NSERC) of Canada, the National

Science Foundation of China under Grants 60905037 and 60802064, and the

Specialized Research Fund for the Doctoral Program of Higher Education of

China under Grant 200806141049.

H. Qu is with the School of Computer Science and Engineering, University

of Electronic Science and Technology of China, Chengdu 610054, China and

also with the School of Engineering, University of Guelph, Guelph, ON N1G

2W1 Canada (e-mail: HongQu@uestc.edu.cn).

S. X. Yang is with the Advanced Robotics and Intelligent System (ARIS)

Laboratory, School of Engineering, University of Guelph, Guelph, ON N1G

2W1 Canada (e-mail: syang@uoguelph.ca).

A. R. Willms is with the Department of Mathematics and Statistics, Univer-

sity of Guelph, Guelph, ON N1G 2W1 Canada (e-mail: awillms@uoguelph.ca).

Z. Yi is with the School of Computer Science, Sichuan University, Chengdu

610054, China.

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TNN.2009.2029858

in 1979 [1], which presented an algorithm to avoid polyhedral

obstacles based on a visibility graph, various methods have

been proposed to solve the robot path-planning problem. Global

methods such as road map [2], cell decomposition [3]–[6], and

distance transform [7] were able to search possible paths in the

whole workspace, although these methods are mainly suitable

to static environments, and are computationally expensive

in complex environments. Many heuristic approaches, such

as potential ﬁeld methods [8]–[13] and the grid-based

algorithm [14]–[16], have been proposed to provide effective

path searching. Some of those methods suffer from undesired

local minima, i.e., the robot may be trapped in some cases

such as with concave U-shaped barriers. In general, the global

approaches would suffer from slow computation for implemen-

tation in complex environments, while the local planners have

difﬁculty to ﬁnd a reasonable solution to some situations with

local minima.

Some new approaches have also been reported in recent years.

Li and Bui [17] proposed a ﬂuid model for robot path plan-

ning in a static environment. Ong and Gilbert [18] proposed a

new model for path planning with penetration growth distance,

which can generate optimal continuous robot paths in static en-

vironments. Oriolo

et al. [19] proposed a model for real-time

map building and navigation for a mobile robot, where a global

path-planning algorithm, a local graph search algorithm, and

several cost functions are used. Hu and Yang [20] proposed an

efﬁcient knowledge-based genetic algorithm for real-time path

planning of mobile robots, where ﬁve genetic operators were de-

signed particularly for robot path planning. Lebedev et al. [21]

presented a dynamic wave expansion model for robot motion

planning in time-varying environments, which is claimed to be

parameter free, and computationally efﬁcient in dynamic envi-

ronments. More recently, Willms and Yang [22], [23] proposed

an efﬁcient dynamic programming algorithm for real-time robot

path planning, which is reported to be suitable to situations

where targets and barriers are permitted to move.

Since the original work of Hopﬁeld [24] in 1985, much

research has been done using neural networks to solve combi-

natorial optimization problems [25]–[27]. Some neural network

models have been proposed to generate real-time robot trajec-

tories. Zalama et al. [28] proposed a neural network model

for mobile robot navigation. Kohonen’s self-organizing map

(SOM)-based model that learns the transformation from the

Cartesian workspace to the joint space of robot manipulators

was studied by Ritter et al. [29]. Zhu and Yang [30] proposed

a SOM-based model for dynamic task assignment and path

planning of multirobots. Glasius et al. [31]–[33] proposed a

Hopﬁeld-type neural network for real-time trajectory genera-

tion with obstacle avoidance in a nonstationary environment.

QU et al.: REAL-TIME ROBOT PATH PLANNING BASED ON A MODIFIED PULSE-COUPLED NEURAL NETWORK MODEL 1725

It is rigorously proved that the generated trajectory does not

suffer from undesired local minima and is globally optimal in a

stationary environment. However, these models require that the

robot dynamic is faster than the target and obstacle dynamics,

and have difﬁculty in dealing with fast changing environments

[34]. Inspired by the dynamic properties of Hodgkin and

Huxley’s membrane model [35] for a biological neural system

and the later developed Grossberg’s shunting model [36], [37],

Yang and Meng [38] proposed a new neural network approach

for dynamic environments. This neurodynamics approach is

later extended to various robot systems [39]–[45], and further

inspires the development of a distance-propagating system for

robot path planning [22], [23]. Low

et al. [47] presented a co-

operative extended Kohonen maps (EKMs) to achieve complex

robot motion, and later they [48] described a distributed layered

architecture for resource-constrained multirobot cooperation.

Those two methods are able to avoid local minima such as

concave obstacles as well as dynamic environments.

A pulse-coupled neural network (PCNN) is a biologically

plausible computational algorithm, which is similar to the

locally excitatory globally inhibitory oscillator network (LE-

GION) model proposed by Wang et al. for real-time image

segmentation, ﬁgure/ground segregation, and many other ap-

plications [49], [50]. PCNNs are capable of emulating the

behavior of cortical neurons as observed in the visual cortices

of cats [51]. Since Johnson’s work [52]–[54], there has been

increased interest in using PCNNs for various applications,

such as target recognition [55], image processing [56], motion

matching [57], pattern recognition [58], and optimization [59].

Some recent research shows that the spatio–temporal dynamics

of PCNNs provide good computational capability for solving

some optimization problems. In 1999, Caulﬁeld and Kinser

[59] presented the idea of utilizing the autowave in PCNNs

to ﬁnd the solution to the maze problem. Their model can

ﬁnd the shortest path quickly and with minimum effort, where

the solution is related to the length of the shortest path and

independent to the path graph complexity. However, many

neurons are needed to ﬁnd the shortest path in large mazes or

graphs, since one pulse of the coupled neuron corresponds to

a unit length of path [60].

In this paper, a novel real-time collision-free robot-path-plan-

ning approach is proposed based on a modiﬁed pulse-coupled

neural network (MPCNN). The proposed model is topologically

organized with only local lateral connections among neurons.

It needs fewer neurons than Caulﬁeld and Kinser’s approach

[59], since the pulse propagation does not correspond to a unit

length of path. Instead, the generated spiking wave in the pro-

posed network spreads at a constant speed so that the time of

travel between two neurons is proportional to the path length

between them. Whenever the sensory systems (either onboard

or installed in the workspace) detect a change in the dynamic

environment, a new path is calculated in the same way. The

computational complexity of the algorithm is only related to the

length of the shortest path, and independent of the workspace

complexity and the number of existing paths in the map. Each

neuron in the proposed model propagates a ﬁring event to its

neighboring neuron without any comparison computations. The

proposed model also works in real time and requires no prior

knowledge of target or barrier movement, no explicit optimiza-

tion of any cost functions, and no explicit searching over the free

workspace or collision paths. It is, therefore, useful for real-time

robot path planning in dynamic environments, without the need

of any learning procedures.

Similar to many existing path-planning methods [21], [22],

[38], in the proposed approach to real-time robot path planning,

the complete knowledge of the current environment is required.

In particular, it is assumed that the locations of the robot, obsta-

cles, and targets are completely and accurately known through

varioussensor measurements,multisensor fusion,and signalpro-

cessing systems. The autonomous navigation of mobile robots is

verycomplicatedandinvolvesmanyissues,suchasreal-timepath

planning, multisensor fusion, signal processing, and motion con-

trol. The sensor placement and multisensor fusion needed to ob-

tain complete environment knowledge, the signal processing re-

quired to remove sensor measurement and communication noise

for accurate environmental information, and the motion control

systems needed to drive the robot wheels are beyond the scope

of this paper. In indoor and closed environments, the complete

knowledge of the workspace can be obtained through several

charge-coupled device (CCD) cameras mounted over the ceiling

and various onboard robot sensors. In outdoor and open envi-

ronments, knowing the environment is a challenging task, which

could possibly be achieved through global positioning system

(GPS), land marks, laser sensors, ultrasonic sensors, and var-

ious other sensors [61]. Related work on real-time path plan-

ning of mobile robots with limited onboard sensory informa-

tion in completely or partially unknown environments is found

in [41], [42], and [62]. Knowing the accurate locations of the

obstacles and robot in the environment at every instant can be

addressed with simultaneous map building/updating and local-

ization methods [41], [63], [64]. Some approaches for real-time

navigation of mobile robots have no explicit global path-plan-

ning algorithms. These employ human-like or biologically in-

spiredstrategies,suchasneurofuzzyandbehavior-basedmethods

[61], [65], where the robot movement is determined by the real-

time sensor measurements and only simple local path planning

is available.

The remainder of this paper is organized as follows. The

proposed modiﬁed PCNN is described and studied theoretically

in Section II. Algorithms for robot path planning, based on

the MPCNN, are presented in Section III. Simulation results

are given in Section IV. Section V discusses parameter setting

for the proposed model. Finally, conclusions are drawn in

Section VI.

II. MPCNN M

ODEL FOR ROBOT PAT H

PLANNING

In this section, an MPCNN model is proposed for real-time

robot path planning. A simple description of the original PCNN

is described in the Appendix. The performance of the proposed

model is analyzed mathematically. In addition, many variables

are deﬁned and used in this section. The main symbols and def-

initions used in this paper are summarized in Table I.

A. Network Architecture

The neural network architecture of the proposed model is a

discrete topologically organized map and can be expressed in a

1726 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 11, NOVEMBER 2009

TABLE I

AIN

SYMBOLS AND

DEFINITIONS

Fig. 1. (a) Network architecture without barrier. (b) Architecture with barrier

at location 7.

ﬁnite-dimensional state space . Each neuron has only local lat-

eral connections with its neighboring neurons, which constitute

a subset

in , as shown in Fig. 1(a).

The neighbors of

are denoted by . Each neuron is

either a free space or a barrier location; the targets and the robot

may occupy any free space. The connection weight

from

the

th neuron to the th neuron is deﬁned to be the Euclidean

distance between the positions

and in the space . If the

th neuron is not in the neighboring set of the th neuron, then

. If the location of the th neuron represents a barrier

location, the connection weight is set as

[Fig. 1(b)].

The weights

are symmetric: , and are independent

of the robot’s motion.

For example, consider two networks, as illustrated in Fig. 1.

There are no barriers in Fig. 1(a). The neighbor set for the

neuron, labeled 6 in this ﬁgure, and the connection weights

from it to all other neurons are

In comparison, with a barrier at location 7, as shown in Fig. 1(b),

the neighbor set for the neuron labeled 6 and the connection

weights from it to all other neurons are

Note that, in general, the connection weight from the th

neuron to different neighboring neurons is not always the same.

For example, for a regular unit square grid, it is either 1 or

In this case, the neighboring set of the

th neuron can be divided

into two subsets

and , deﬁned by

For example, as illustrated in Fig. 1(a), , and are

B. Notions and Deﬁnitions

Before discussing the model itself, some notations and def-

initions about neuron ﬁring and the ﬁring time are deﬁned as

follows.

In the model, each neuron has a single output

Deﬁnition 1: A neuron is said to ﬁre at time

,if ,

such that

when

This time is denoted as .

Except for the case where a target is located at the neuron’s

location, the neuron will not ﬁre until after one of its neighbors

has ﬁred. For any given neuron

, the ﬁrst neuron in its neighbor

set

to ﬁre is denoted as , and the ﬁring time of this neuron

is denoted as

.If and if is determined directly

, neuron is said to ﬁre on the stimulation of neuron ,

and neuron

is called the parent of . In this case, is denoted

and is denoted as .

Sometimes the parent of neuron

can be changed by the ﬁring

of some other neuron in

. For example, at time ﬁres

and becomes the parent of neuron

, preparing to ﬁre at some

time in the future, say

. If at some time before a neuron in

other than ﬁres, and if, in the absence of neuron , the

ﬁring of neuron

would stimulate neuron to ﬁre before , then

becomes the new parent of neuron . In this situation, is

until time at which point becomes .

Deﬁnition 2: For any neuron

, all neurons that can

potentially become the parent of neuron

are said to be in the

changing set of neuron

, denoted as .

Note that

is time dependent. Initially, all neurons in

are in , but after time only those neurons that could

stimulate

to ﬁre sooner are in the set. As approaches the

ﬁring time for

, the set becomes empty. Particularly, for

a square grid with connections as shown in Fig. 1,

can

be nonempty after time

only if , and further,

for , where is some time prior

determined by the parameters of the system.

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